Calculus Answers

The region bounded by the graphs of y= x² and y= x+2

A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with water. Find the work required to pump all the water over the upper rim.

(Assuming the tank is half-filled with water)

Assume that 10 ft-lb of work is required to stretch a spring 1 ft beyond its natural length. What is the spring constant?

A spring exerts a force of 100 N when it is stretched 0.2 m beyond its natural length. How much work is required to stretch the spring 0.8 m. beyond its natural length?

A flat rectangular plate is submerged horizontally in water

a. Find the force (in lb) and the pressure (in lb/ft²) on the top surface of the plate if its area is 100 ft² and the surface is at a depth of 5 ft.

b. Find the force (in N) and the pressure (in Pa) on the top surface of the plate if its area is 25 m² and the surface is at a depth of 10 m.

Let f(x,y)={y^3/x^2+y^2 , 0 otherwise if (x,y) is not =(0,0) show that f is continuous but not differentiable at (0,0)

Check whether limit of the function of f(x,y)=4x^5y/x^10+3y^2 exists as (x,y) tends to (0,0).

Find the cylindrical coordinates of the points where the cartesian coordinates are i)(3,3,4) ii) (√5,1,2)